機械学習モデルからの知識抽出と生命情報学への応用

京都大学新制・課程博士博士(情報学)甲第23397号情博第766号新制||情||131(附属図書館)京都大学大学院情報学研究科知能情報学専攻(主査)教授 阿久津 達也, 教授 山本 章博, 教授 鹿島 久嗣学位規則第4条第1項該当Doctor of InformaticsKyoto UniversityDFA

Maximum likelihood estimation of an unknown change-point in the parameters of a multivariate Gaussian series with applications to environmental monitoring

The computable expressions for the asymptotic distribution of the change-point maximum likelihood estimator (mle) were derived when a change occurred in the mean and covariance matrix at an unknown point of a sequence of independently distributed multivariate Gaussian series. The derivation was based on ladder heights of Gaussian random walks hitting the half-line. We then demonstrated that change in a single parameter or change-point analysis in a univariate series can be derived as special cases. A simulation study was carried out to investigate the robustness of the asymptotic distribution to departure from normality, the sample size, location of change-point and amount of change under the multivariate and univariate case. The comparison of the asymptotic mle with Cobb's conditional MLE and Bayesian estimation method using non-informative prior and conjugate prior was also carried out in the simulation study. The asymptotic distribution of the change-point mle was used to compute the confidence interval of the change-point of the stream flows at Northern Quebec Labrador Region and zonal annual mean temperature deviations

Difference of sequence topologies

We argue that topology can be interpreted as an area of mathematics studying preserved properties under an equivalence relation, and representation, classification and comparison of the corresponding equivalence classes. With this understanding, we can generalize ideas in topology to non-geometric objects. In this paper, which presents an example of such generalization, we define a sequence topology to be an equivalence class of finite integer sequences of the same length under relabeling or permutations. The difference for a set of finite integer sequences of the same length is defined to be the number of mismatches in the sequences. While the difference for a set of sequence topologies is defined to be the minimum difference over all sets of sequences constructed by choosing one sequence from each sequence topology. We count the number of different sequence topologies of a given length and a set of possible labels and determine the minimum upper bound of the difference for sequence topologies. Finally, we compute the exact difference for a set of sequence topologies of the same length.Comment: 11 page